Systoles on Riemann surfaces
type: Item
instance of: scholarly article
title: Systoles on Riemann surfaces
zbMATH Open document ID: 0819.30027
DOI: 10.1007/BF02568209
published in: Manuscripta Mathematica
publication date: 1995-02-20T00:00:00Z
full work available at URL: https://eudml.org/doc/156033
review text: The author studies Riemann surfaces with constant curvature \(-1\) and signature \((g,n)\) that is with genus \(g\) and \(n\) boundary components which here are simple closed geodesics or cusps. A systole of a surface is a shortest closed geodesic which is not a boundary component. The paper contains numerous results concerning the following two main problems: I: For a fixed signature \((g,n)\) search the surfaces with a systole of maximal length. II: For a fixed signature \((g,n)\) search the surfaces with the maximal number of systoles. For example new global and local maximal surfaces of small genus for problem I are presented. A general theory and examples are given for problem II. It is completely solved for genus 2 and an upper bound for the number of systoles of closed surfaces is proved. Here definitely is not enough space to mention all the ideas and results in this paper. You should read it!
Mathematics Subject Classification ID: 30F45
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 724669
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: geodesics
author: Paul Schmutz Schaller
reviewed by: Steffen Timmann
MaRDI profile type: Publication
cites work: Q4039225
cites work: Q4340763
cites work: Asymmetric combinatorially-regular maps
cites work: Q4039784
cites work: Filling Riemannian manifolds
cites work: Q4340764
cites work: Q3751649
cites work: Infinite families of surface symmetries
cites work: Riemann surfaces with shortest geodesic of maximal length
cites work: Congruence subgroups and maximal Riemann surfaces
cites work: Arithmetic Fuchsian groups and the number of systoles
cites work: Compact Riemann surfaces with many systoles
Wikidata QID: Q125768318
OpenAlex ID: W2039421340
description: scientific article; zbMATH DE number 724669